Experimentally well-constrained masses of 27P and 27S: Implications for studies of explosive binary systems

L.J. Sun a,b,c,1, X.X. Xu a,b,d,1,∗, S.Q. Hou d,x,1, C.J. Lin a,e,∗∗, J. José f,g,∗∗∗, J. Lee b,∗∗∗∗, J.J. He h,i, Z.H. Li j, J.S. Wang k,d,i, C.X. Yuan l, F. Herwig m,n,x, J. Keegans o,x, T. Budner p,q, D.X. Wang a, H.Y. Wu j, P.F. Liang b, Y.Y. Yang d, Y.H. Lam d, P. Ma d, F.F. Duan r,d, Z.H. Gao d,r, Q. Hu d, Z. Bai d, J.B. Ma d, J.G. Wang d, F.P. Zhong a,e, C.G. Wu j, D.W. Luo j, Y. Jiang j, Y. Liu j, D.S. Hou d,i, R. Li d,i, N.R. Ma a, W.H. Ma d,s, G.Z. Shi d, G.M. Yu d, D. Patel d, S.Y. Jin d,i, Y.F. Wang t,d, Y.C. Yu t,d, Q.W. Zhou u,d, P. Wang u,d, L.Y. Hu v, X. Wang j, H.L. Zang j, P.J. Li b, Q.Q. Zhao b, H.M. Jia a, L. Yang a, P.W. Wen a, F. Yang a, M. Pan w,a, X.Y. Wang w, Z.G. Hu d, R.F. Chen d, M.L. Liu d, W.Q. Yang d, Y.M. Zhao c


Introduction
Type I X-ray bursts (XRB) and classical novae are the two most frequent types of thermonuclear stellar explosions in the Galaxy. They are powered by thermonuclear runaways occurring in the accreted envelopes of compact objects in stellar binary systems. In the case of XRBs, hydrogen-or helium-rich material is transferred from a low mass main sequence or red giant star onto the surface of a neutron star, while nova explosions occur in a similar system with a white dwarf in place of the neutron star. As they are driven by a suite of nuclear processes, accurate nuclear physics inputs such as β-decay rates, masses, and nuclear reaction rates of proton-rich isotopes are needed to model the energy production and nucleosynthesis in these explosions. Our understanding of these systems has greatly improved with time, but despite decades of work, many open questions remain [1][2][3][4][5][6].
A recent systematic investigation of the impact of nuclear mass uncertainties on XRB models found that the mass uncertainties of 27 P can strongly affect the model predictions of the burst light curve and the composition of the burst ashes in a typical mixed H/He burst [7]. This study was carried out based on the mass excess of ( 27 P) = −722 (26) keV reported by the 2012 Atomic Mass Evaluation (AME2012) [8], and the latest AME2016 still adopted the same value [9]. Since then, a 27 S β-decay measurement using an optical time projection chamber [10] reported a mass excess of ( 27 P) = −640(30) keV, which was inconsistent with the AME value. A more recent ( 27 P) = −685(42) measured via isochronous mass spectrometry in the Cooler Storage Ring [11] was not sufficiently precise to resolve the existing discrepancies. Additionally, 27 S was considered to be a waiting-point nucleus in the thermonuclear reaction network, and its mass uncertainty could impact the nucleosynthesis in some XRB model calculations [12,13] based on the mass excess of ( 27 S) = 17540(200) keV in AME2003 [14]. Nevertheless, the 27 S mass is unknown experimentally and both AME2012 and AME2016 roughly estimated the mass to be ( 27 S) = 17030(400) keV [8,9]. Hence, experimental efforts should be made to better quantify the mass excesses of 27 P and 27 S. Furthermore, the origin of large amounts of 26 Al in the interstellar medium of the galaxy has been a focus of interdisciplinary investigations in astronomy, astrophysics, and nuclear physics [15]. The nova nucleosynthesis of 26 Al is dominated by a reaction sequence of 24 Mg(p, γ ) 25 Al(β + ) 25 Mg(p, γ ) 26 Al(p, γ ) 27 Si, but this sequence may be bypassed through 25 Al(p, γ ) 26 Si(p, γ ) 27 P [16,17]. Under a wide temperature range of 0.1-2 GK, the 26 Si(p, γ ) 27 P reaction rate was found to be dominated only by a single resonant proton capture on the 26 Si ground state to the 3/2 + first excited state in 27 P. According to previous nova nucleosynthesis calculations [18], the 26 Si(p, γ ) 27 P rate was not expected to play a critical role, but it should be noted that a complete experimental constraint on the thermonuclear 26 Si(p, γ ) 27 P rate had never been set. Estimates of those key resonance strengths have relied on limited experimental information on the structure of 27 P, supplemented by shell model calculations or the mirror nucleus information [19][20][21][22][23][24][25][26][27][28][29]. A reevaluation of the role of the 26 Si(p, γ ) 27 P reaction with more accurate 27 P mass and resonance properties may benefit the long-standing study of the galactic 26 Al origin.
Recently, we reported the highest-statistics β-decay spectroscopy of 27 S to date [30]. The charged particles and γ rays emitted in the β decay of 27 S were measured simultaneously for the first time, allowing us to determine an accurate 27 P mass excess and to place a constraint on the 27 S mass excess based on experimental results. In this Letter, we further investigate the astrophysical impact of the newly determined masses using the XRB and nova models.

Mass evaluation
The present data set and analysis procedures have been detailed in Ref. [30]. The main nuclear structure information relevant to the astrophysics topic is summarized in Fig. 1 and are briefly discussed here for completeness. The mass excess of the 27 P is determined to be −659(9) keV by combining the measured excitation energy of 1125(2) keV and the proton-decay energy of 318(8) keV of the first excited state in 27 P with the well-known mass excesses of 26 Si and 1 H from AME2016 [9]. The γ -ray energy of 1125(2) keV has been confirmed by a recent in-beam γ -ray spectroscopy [31], which reported two γ -ray energies of 1125(6) keV and 1119(8) keV. Previously, the AME2003 value of ( 27 P) = −717(26) keV [14] was the weighted average of ( 27 P) = −753(35) keV measured using the 32 S( 3 He, 8 Li) 27 P reaction [32] and ( 27 P) = −670(41) keV measured using the 28 Si( 7 Li, 8 He) 27 P reaction [19]. The AME2012 reevaluated the latter value to be ( 27 P) = −683(41) keV based on a new 8 He mass measured by Penning trap mass spectrometry [33] and updated the weighted average mass to be ( 27 P) = −722(26) keV [8]. This evaluation remained unchanged in the AME2016 [9]. As shown in Fig. 2, the mass excess of 27 P determined in our work represents the most precise 27 P mass measurement to date. Our value deviates from the AME2016 value by 63 keV (2.3σ ) while improving the precision by a factor of 3. Since the release of AME2016, all three independent measurements [10,11,30] are in good agreement, indicating a need for the reevaluation of the 27 P mass in the next version of AME. Theoretical 27 P mass values show even large discrepancies than experimental values, such as, ( 27 P) = −716(7) keV calculated using the isobaric mass multiplet equation [7], ( 27 P) = −779(289) keV [34], −565(44) keV [35], −551(87) keV [35], and −731 keV [36] calculated using mirror nuclei relations. Hence, our result provides  27 S. The drawing is not to scale. All the energies, mass excesses, and intensities labeled in the scheme are deduced from our work [30], except for the well-known mass excesses of 25 Al and 26 Si from AME2016 [9]. See text for details.

Fig. 2.
Mass excesses of 27 P measured in our work compared with the recommended value from AME [14,8,9] and values previously measured by Beneson et al. [32], Caggiano et al. [19], Janiak et al. [10], and Fu et al. [11], with our uncertainty indicated by the dashed lines. All mass values have been rounded to the closest integer for simplicity. an important benchmark against which local nuclear mass models can be tested and constrained, thereby improving the accuracy and predictive power of models.
The two-proton emission from the T = 5/2 isobaric analog state (IAS) in 27 P to the 25 Al ground state was identified in previous 27 S decay studies [37,38], whereas the two measured center-of-mass energies, E 2p = 6410(45) keV [37] and E 2p = 6270(50) keV [38], were mutually inconsistent by 2.1σ . This two-proton energy was measured to be 6372 (15) keV in our work [30], which falls between these two previous results [37,38]. It is worth mentioning that we further investigate the relationship between the energy loss, position, and path length of the escaping particles in different silicon detectors to verify that this is indeed two-proton emission rather than one-proton emission at the same energy [39]. Combining the energy of two-proton emission E 2p = 6372(15) keV with the well-known mass excesses of ( 25 Al) = −8915.97(6) keV and ( 1 H) = 7288.97061(9) keV from AME2016 [9], the mass excess of the T = 5/2 IAS in 27 P is determined to be 12034 (15)

Thermonuclear 26 Si(p, γ ) 27 P reaction rate
The Gamow window for the 26 Si(p, γ ) 27 P reaction is calculated from a numerical study of the relevant energy ranges for astrophysical reaction rates [41]. The second and third resonances (5/2 + 1 and 5/2 + 2 ) enter the Gamow window at temperatures above 1.2 GK and 2.0 GK, respectively, and their contributions have proven to be negligible compared to the first resonance (3/2 + 1 ) at 318(8) keV [22,23,30]. At any given temperatures below 2.0 GK, the first resonance is always the closest one to Gamow peaks. Its proton partial width is calculated to be p = 2.55(74) meV using the relation γ = p × I γ /I p , with the γ -ray partial width γ = 3.43(170) meV adopted in the compilation [42]. Here, the ratio of the γ -ray branch to the proton branch of I γ /I p = 1.35 (39) has been determined experimentally for the first time in our work [30].
Thus, a resonance strength of ωγ = 2.92(191) meV can be derived by taking into account the partial widths and the known spins of the resonance, proton, and the ground state of 26 Si. By combining these values with the existing parameters for the two trivial 5/2 + resonances and the direct-capture component evaluated by Iliadis et al. [42], the total rate is determined based on Monte Carlo techniques [43], where uncertainties are rigorously defined. This result agrees with the rate computed using a simple numerical integration [30].
Currently, the 26 Si(p, γ ) 27 P reaction rate evaluated by Iliadis et al. [42,44] is recommended in both REACLIB [45] and STARLIB [46] and universally adopted in various astrophysical model calculations. As shown in Fig. 3, the present rate is up to two orders of magnitude lower than the recommended rate in the temperature range 0.06 < T < 0.3 GK (typical for nova nucleosynthesis).
Our rate is higher than the recommended rate by up to a factor of 4 around 2.0 GK (typical for XRB nucleosynthesis). The deviation is due to the larger resonance energy and strength for the 3/2 + resonance derived from our experiment. It can be seen that the present rate has much smaller uncertainties than the recommended one almost over the entire temperature range, except that the present reaction rate follows the trend of the recommended one below 0.06 GK where the direct-capture uncertainty dominates.

Astrophysical implications for XRB model
We have investigated the impact of the present mass excesses of 27 P and 27 S and the 26 Si(p, γ ) 27 P reaction rate on the composition of XRB nucleosynthesis zone using the one-zone postprocessing nucleosynthesis code, a branch of the NuGrid framework [47], together with a trajectory K04 from Ref. [48]. The comparison to the calculation using the rates and masses from databases [9,44] are shown in Fig. 4. No visible change is found in the two nuclear energy generation rates during the burst, but the mass fractions of 26 Al and 26 Si, therefore the A = 26 abundance, are clearly increased. This change is mainly attributed to the reverse 27 P(γ , p) 26 Si rate, which exponentially depends on the reaction Q -value. The higher mass excess of 27 P results in a significant increase in 27 P(γ , p) 26 Si rate, which will impede the proton capture process and leaves more 26 Si and its corresponding β-decay daughter 26 Al. Due to the neutron star gravitational potential, most of the burst ashes remain on the neutron star surface and replace the crust of the neutron star, and thus, they will have an impact on the accreted crusts thermal and compositional structure [49]. A proper understanding of the ashes produced by XRBs is also important for the modeling of the crust evolution of accreting neutron stars [50].
Similarly, the higher 27 S mass value obtained in our work would also result in a much stronger reverse 27 S(γ , p) 26 P rate which can effectively impact the final yield of 27 S. Our XRB model calculation shows that the final abundance ratio 27 S/ 26 P is 3.8 and 3500 using the 27 S mass value from AME2003 [14] and AME2012 (or 2016) [8,9], respectively, compared to the 27 S/ 26 P ratio of 0.4 using our 27 S mass value. Previously, 27 S was considered to be a waiting-point nucleus in the rapid proton capture process [12,13]. However, the present significant abundance change strongly implies that 27 S should not be regarded as a waiting-point nucleus.

Astrophysical implications for nova model
The impact of the aforementioned nuclear physics input on nova nucleosynthesis, and in particular on the synthesis of 26 Al, has been examined through a series of hydrodynamic simulations. To this end, a suite of evolutionary sequences of nova outbursts hosting ONe white dwarfs of 1.15, 1.25, and 1.35 M have been computed with the spherically symmetric, Lagrangian, hydrodynamic code SHIVA, extensively used in the modeling of novae and XRBs (see Refs. [1,6] for details). Results have been compared with those obtained in three additional hydrodynamic simulations for the same white dwarf masses described above and the same physics inputs except for the 26 Si(p, γ ) 27 P reaction rate, which was taken from the evaluation [44]. As confirmed by these simulations, the dominant destruction channel for 26 Si in nova outbursts occurs via its β + decay to the isomeric state of 26 Al, which subsequently decays to the ground state of 26 Mg. No significant change in the element production in the Mg-P mass region was found when using the 26 Si(p, γ ) 27 P reaction rate from Iliadis et al. [44] or from the present work. Moreover, no significant changes were found when variations in this rate within uncertainties were used [51]. The dominant destruction mode of 26 Si under nova temperatures is confirmed to be β + decay rather than the 26 Si(p, γ ) 27 P reaction.
Compared to the result using the recommended Iliadis et al. [44] rate, the contribution of classical nova outbursts to the galactic 26 Al mass is only marginally increased by about 0.5%. This verifies previous predictions of the nova contribution to the synthesis of galactic 26 Al [6,52,53] and places the expected 26 Al/ 27 Al ratios in presolar grains of a inferred nova origin on a more solid experimental ground [54].

Conclusion
Based on the β-decay spectroscopy of 27 S, we have determined the mass excess of 27 P, constrained the mass excess of 27 S, and computed the 26 Si(p, γ ) 27 P reaction rate using the Monte Carlo method. A series of astrophysical model calculations incorporating these quantities have been performed. Although the mass value determined in this work has no significant effects on the energy production in XRB, the mass fractions of 26 Al and 26 Si at the end of the burst are found to be increased by a factor of 2.4. The XRB model calculations using our 27 S mass value also indicate that 27 S is not a significant waiting point, contrary to the previous expectation [13]. The nova model calculations confirm the previous predictions of the nova contribution to the synthesis of galactic 26 Al.
The 9-keV uncertainty in the present mass excess of 27 P is dominated by the uncertainty in the β-delayed proton energy measured by silicon detectors. To further improve the precision of the 27 P mass, a direct measurement using Penning trap mass spectrometry facilities would be desirable [55].

Acknowledgments
We acknowledge the dedicated effort of the HIRFL beam physicists and operations staff for providing high-quality beams. We gratefully acknowledge Christian Iliadis for the reaction rate calculations. We would like to thank Zhihong Li, Bing Guo, Hendrik